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A302355
a(n) = coefficient of x^n in the n-th iteration (n-fold self-composition) of the g.f. of triangular numbers (A000217).
1
1, 6, 72, 1390, 37515, 1307691, 56000728, 2847503268, 167737660533, 11236731677941, 843757483026150, 70200772129462767, 6410711453857626149, 637516967943664853331, 68581800216461580653064, 7935677122691714769565104, 982824624566131043920711329, 129722104862557293606783635718
OFFSET
1,2
EXAMPLE
The initial coefficients of successive iterations of g.f. A(x) = x/(1 - x)^3 are as follows:
n = 1: 0, (1), 3, 6, 10, 15, ... g.f. A(x)
n = 2: 0, 1, (6), 30, 137, 588, ... g.f. A(A(x))
n = 3: 0, 1, 9, (72), 543, 3933, ... g.f. A(A(A(x)))
n = 4: 0, 1, 12, 132, (1390), 14208, ... g.f. A(A(A(A(x))))
n = 5: 0, 1, 15, 210, 2840, (37515), ... g.f. A(A(A(A(A(x)))))
MATHEMATICA
Table[SeriesCoefficient[Nest[Function[x, x/(1 - x)^3], x, n], {x, 0, n}], {n, 18}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 06 2018
STATUS
approved